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Ms. Williams’s Analysis: An Instructional Minicase on Interpreting Student Work About the Simplification of Exponential Expressions MKT PST

Howell, Heather; Lai, Yvonne; Olah, Leslie Nabors; DeLucia, Maria; Kim, Eun Mi
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Mathematics Education, Exponential Expressions, Mathematical Knowledge for Teaching (MKT), Student Experience, Student Performance, Student Assessment, Student Teacher Relationship, Teacher Preparation, Preservice Teacher Education, Teacher Support, Curriculum Materials, Curriculum Development, Mathematical Reasoning, Generating Explanations, Curriculum Objectives


There is a broad consensus that beginning teachers of mathematics need a strong foundation in mathematical knowledge for teaching (MKT), defined as the mathematical knowledge required to recognize, understand, and respond to the mathematical work of teaching in which one must engage. One recurrent challenge in teacher education is how to provide support for preservice teachers (PSTs) to acquire such competencies. Recent trends toward practice-based teacher education support the idea of engaging novice teachers in activities that are purposefully constrained to a core teaching practice. Ms. Williams’s Analysis is an abbreviated instructional case (i.e., a minicase) based on an assessment scenario in which PSTs are asked to attend to two students’ application of the laws of exponents in the course of simplifying an exponential expression. PSTs are asked to judge the mathematical validity of the students’ explanations as a way of further developing their own MKT.

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